If you have built Clang/LLVM from the supplied makefile in ClangKit/LLVM, then everything should be fine.
The makefile copies the new libraries to the location expected by the Xcode project.

So simply rebuild ClangKit from Xcode...

And where can I view these libraries in the Xcode project? Linked frameworks and libraries?

They are set in the target's build settings (OTHER_LDFLAGS).

Even though I've done that, I am still getting the following verbose message in the CKDiagnotic:
ignoring nonexistent directory "/Users/Gurmeher/Library/Developer/Xcode/DerivedData/ClangKit-ddxafeblyiqsqwagblctgyofkfet/Build/Products/Debug/ClangKit.framework/Versions/A/clang/3.7.0/include"

Must there be a clang directory in the ClangKit Framework's root?

No, there's not... Clang include are not copied into the framework.
Looks like you modified the project to copy them, hence the error...

The include directory is not being copied into the framework.
It seems that the CKTranslation is looking for include directory at the root folder of the framework, and cannot find the same.

I have no idea about what you are trying to achieve.

If you don't give me some context, I won't be able to help you...

• Are you experiencing a compile-time issue, or a runtime issue?
• Why are you rebuilding LLVM?
• How did you modified the project?
• ...

I cannot read your mind...

• I have built the ClangKit(framework) target from Xcode.
• I have then run the ClangKitTest target.
• The C code compiles without any diagnostics.
• However, when the Objective-C Code compiles with the diagnostic: "'stdarg.h' file not found"
• On passing the "-v" flag in the CKTranslationUnit arguments, I am getting the message:
  ignoring nonexistent directory "/Users/Gurmeher/Library/Developer/Xcode/DerivedData/ClangKit-ddxafeblyiqsqwagblctgyofkfet/Build/Products/Debug/ClangKit.framework/Versions/A/clang/3.7.0/include"

Ok, so this is a runtime issue.
Basically, it means that ClangKit is working fine, if it gives you diagnostics.

Again, as mentioned in your previous issue, if <stdarg.h> is not found, it means your development environment is not correctly set-up.
And ClangKit warns you about this, as your compiler would do.

What version of macOS/Xcode are you using?

The latest of both.
Also, I have tried running the app on various systems but with no success.

Ok, I'll see if I can update the example, so it's more clear.

The error you are getting just means you need to supply additional arguments to the translation unit, as you would do for a usual compiler.

OK, I've added an example in 6e2a2f5.
It gets the correct Clang include paths from the Xcode default toolchain, if available.

Depending on your Xcode version, ClangKit may report other diagnostics, because the LLVM libraries need to be updated for the latest macOS SDKs.
But as it seems you've updated them, this shouldn't be an issue.

I'll try to update them, but I'm on other things right now.

On downloading and running the latest ClangKit build, I am getting the following verbose message on compilation of the Objective C Code through CKTranslationUnit:

ignoring nonexistent directory "/Users/Gurmeher/Library/Developer/Xcode/DerivedData/ClangKit-fawyikkexkgzgxawdfflitbxsezj/Build/Products/Debug/ClangKit.framework/Versions/A/clang/3.7.0/include"
#include "..." search starts here:
#include <...> search starts here:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/lib/clang/8.1.0/include
/usr/local/include
/usr/include
/System/Library/Frameworks (framework directory)
/Library/Frameworks (framework directory)
End of search list.
ignoring nonexistent directory "/Users/Gurmeher/Library/Developer/Xcode/DerivedData/ClangKit-fawyikkexkgzgxawdfflitbxsezj/Build/Products/Debug/ClangKit.framework/Versions/A/clang/3.7.0/include"
#include "..." search starts here:
#include <...> search starts here:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/lib/clang/8.1.0/include
/usr/local/include
/usr/include
/System/Library/Frameworks (framework directory)
/Library/Frameworks (framework directory)
End of search list.

Also, the CKDiagnostic objects returned from the CKTranslation are as follows:

2017-05-10 17:11:02.145609 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015a9a80>: Error[19:21] - expected a type
2017-05-10 17:11:02.145699 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.145778 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015a9ee0>: Error[25:28] - expected a type
2017-05-10 17:11:02.145822 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.145874 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015aa340>: Error[32:4] - expected a type
2017-05-10 17:11:02.145889 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.145908 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015aa7a0>: Error[44:12] - unknown property attribute 'class'
2017-05-10 17:11:02.145920 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.145939 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015aac10>: Error[57:4] - expected a type
2017-05-10 17:11:02.145950 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.145967 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ab070>: Error[58:4] - expected a type
2017-05-10 17:11:02.145979 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.145995 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ab4d0>: Error[7:15] - expected ';' after @Class
2017-05-10 17:11:02.147111 ClangKitTest[796:17080] FixIts: (
"<CKFixIt: 0x1015a9760>: ;"
)
2017-05-10 17:11:02.147153 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ab970>: Error[7:16] - cannot find protocol declaration for 'ObjectType'
2017-05-10 17:11:02.147204 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147286 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015abdf0>: Error[34:25] - cannot find protocol declaration for 'ObjectType'
2017-05-10 17:11:02.147310 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147341 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ac270>: Error[34:37] - expected identifier or '('
2017-05-10 17:11:02.147360 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147397 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ac6d0>: Error[36:4] - expected a type
2017-05-10 17:11:02.147454 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147517 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015acb30>: Error[40:25] - cannot find protocol declaration for 'ObjectType'
2017-05-10 17:11:02.147539 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147569 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015acfb0>: Error[40:1] - duplicate interface definition for class 'NSEnumerator'
2017-05-10 17:11:02.147587 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147761 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ad430>: Error[40:37] - method type specifier must start with '-' or ' '
2017-05-10 17:11:02.147789 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147832 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ad8b0>: Error[40:38] - expected a type
2017-05-10 17:11:02.147909 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.147962 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015add10>: Error[42:1] - expected selector for Objective-C method
2017-05-10 17:11:02.147985 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.148016 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ae180>: Error[42:36] - cannot find protocol declaration for 'ObjectType'
2017-05-10 17:11:02.148077 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.148134 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015ae600>: Error[17:4] - expected a type
2017-05-10 17:11:02.148163 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.148198 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015aea60>: Error[30:42] - expected a type
2017-05-10 17:11:02.148244 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.148328 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015aeec0>: Warning[9:16] - unused variable 'x'
2017-05-10 17:11:02.148461 ClangKitTest[796:17080] FixIts: (
)
2017-05-10 17:11:02.148498 ClangKitTest[796:17080] Diagnostic: <CKDiagnostic: 0x1015af320>: Warning[10:16] - unused variable 'f'
2017-05-10 17:11:02.148519 ClangKitTest[796:17080] FixIts: (
)

That's what I told you in my previous comment.

I have rebuilt the latest LLVM and Clang from source. However, I am unable to find the static libraries from the build named as follows:
libclang.a

In the new build? Have you tried removing it from the LD flags?

Do you mean removing -libclang from the LDFlags?